A (4n - 4)-Bit Representation of a Rectangular Drawing or Floorplan

Authors:
Toshihiko Takahashi;Ryo Fujimaki;Youhei Inoue
Affiliations:
Niigata University, Niigata, Japan 950-2181;Niigata University, Niigata, Japan 950-2181;Renesas Technology Corp., Tokyo, Japan 100-0004
Venue:
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Year:
2009

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Abstract

A subdivision of a rectangle into rectangular faces with horizontal and vertical line segments is called a rectangular drawing or floorplan. Yamanaka and Nakano published a (5n - 5)-bit representation of a rectangular drawing, where n is the number of inner rectangles. In this paper, a (4n -4)-bit representation of rectangular drawing is introduced. Moreover, this representation gives an alternative proof that the number of rectangles with n rectangles R (n ) ≤ 13.5 n - 1.